Mladen Vassilev–Missana

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 22, 2016, Number 2, Pages 4—9

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## Details

### Authors and affiliations

Mladen Vassilev–Missana

*5 Victor Hugo Str, Ap. 3
1124 Sofia, Bulgaria
*

### Abstract

Let *n* > 3 be arbitrary integer. In the present paper it is shown that if *K* is an arbitrary circle and *M _{i}*,

*i*= 1,…,

*n*are points on

*K*, dividing

*K*into

*n*equal arcs, then for each point

*M*on

*K*, different from the mentioned above, at least of the distances |

*MM*| are irrational numbers.

_{i}### Keywords

- Distance
- Irrational number
- Circle

### AMS Classification

- 97G40
- 11XX

### References

- Coolidge, J. L. (1939) A Historically Interesting Formula for the Area of a Quadrilateral. Amer. Math. Monthly, 46, 345–347.
- Nagell, T. (1951) Introduction to Number Theory. Wiley, New York.
- Mason, J. C., & Handscomb, D. C. (2003) Chebyshev Polynomials. CRC Press, New York.

## Related papers

## Cite this paper

APAVassilev–Missana, M. (2016). On irrationality of some distances between points on a circle. Notes on Number Theory and Discrete Mathematics, 22(2), 4-9.

ChicagoVassilev–Missana, Mladen. “On Irrationality of Some Distances between Points on a Circle.” Notes on Number Theory and Discrete Mathematics 22, no. 2 (2016): 4-9.

MLAVassilev–Missana, Mladen. “On Irrationality of Some Distances between Points on a Circle.” Notes on Number Theory and Discrete Mathematics 22.2 (2016): 4-9. Print.